1. Field of the Invention (Technical Field)
The present invention relates to Flight Management Systems (FMS) and more particularly to a method for calculating an intercept position where one aircraft will intersect with a target aircraft.
2. Background Art
The most common rendezvous (RZ) intercept computation is to use the spherical triangle formula. With the assumption of small angles, the non-linear spherical formula can be converted to a quadratic formula that can be solved easily. There are three major problems with the prior art approach. This small angle approximation limits the rendezvous distance to less than 600 nautical miles (NM). Secondly, the wrong solution is computed when two aircraft are flying on the same path where the triangle becomes a straight line and the spherical triangle formula is no longer valid. Third, no adjustment is made when the intercept position is in a polar region where the earth is not a perfect sphere. These are the problems the present invention solves.
These problems occur in C130J-Communication Navigation Identification (C130J-CNI), C27J-Communication Navigation Identification (C27J-CNI), C141-GPS Enhanced Navigation System (C141-GENE), and Core Flight Management System (Core FMS). They use the same method, the spherical triangle formula, to compute the rendezvous intercept position. For example, the method used in C130J-CNI FMS to compute the rendezvous intercept position can be re-derived as follows:Cos a=cos b·cos c+sin b·sin c·cos A  (1)
where a=v1·t/R c=v2·t/R b=d/R
d: a great circle distance between two initial aircraft positions
R: average radius of Earth
A: angle between b and c
Assuming a and c are small, plug a, b, c into (1), and use second order approximation for sin and cos functions, we get the following equation:A0·t2+B0·t+C=0  (2)whereA0=v12−v22·cos bB0=2·v2·sin b·cos A C0=2·cos b−2
If B02−4·A0·C0≧0, the smaller non-zero positive solution of equation (2) is the intercept position.
The C130J-CNI Rendezvous calculation is based on two assumptions:
a) The current aircraft, target aircraft, and interception positions form a spherical triangle, not a straight line; and
b) The sides of the triangle need to be less than 600 NM (due to the small angle approximation).
Therefore, the prior art systems will fail when the two aircraft are flying on the same track regardless what direction the aircraft fly. In this case the law of cosine does not work. The assumption of small angles a and c (from the equations above) limits the rendezvous distance to 600 NM (equivalent to 10 degrees). The law of cosine works in a perfect sphere but not in the polar regions of the earth.
The present invention is not based on these assumptions, so it provides a solution for any scenario (longer than 600 NM and/or when the two aircraft are flying on the same track). The present invention uses a Sodanos equation (The Journal of the International Association of Geodesy in March 1965, and a supplement was published in the same publication in September of 1967) to compute the great circle distance d between two initial aircraft positions. The present invention consistently provides a rendezvous intercept position with the same selectable accuracy even when the rendezvous distance is longer 600 NM, the intercept position is in a polar region, or the two aircraft flying on the same path.
U.S. Pat. No. 6,271,768 B1, discloses the method to display the formation of aircraft within a distributed collision avoidance and control among multiple aircraft within formation which use a passive Traffic Alert and Avoidance System (TCAS) and Mode-S data link transponder. The display denotes the relative altitude as well as relative velocity of the formation follower aircraft with respect to the lead formation aircraft. This system is directly related to the patent mentioned below which describes the method of determining the aircraft placement within the formation.
U.S. Pat. No. 6,459,411 B2, discloses a method to offer distributed collision avoidance and control amid multiple aircraft within formation for use with a passive Traffic Alert and Avoidance System (TCAS) and Mode-S data link transponder. This system allows for close formation flights among multiple aircraft without needless traffic advisories. These close formation flights are made possible through the use of a Mode-S transponder which is used to process data such as aircraft position and pass data such as steering commands between aircraft. Where as this system deals with maintaining separation of aircraft within a formation, the current invention deals with the computation of an intercept location of two aircraft and thus is extremely different.
U.S. Pat. No. 6,646,588 B2, discloses a solution for implementing a midair collision avoidance system (MCAS). This system is comprised of a tactical module, which is used in conjunction with air traffic management to offer quick-time response, diminished jamming and interference, and minimized detection beyond 10 miles or so. The tactical module can be used to provide display and control guidance to support rendezvous. This system is therefore, used to aid in a rendezvous, but is not directly needed to determine the rendezvous position. Thus, this system has no relevance to the solution proposed in the current invention.